Subgroups — #44526149

Order 30944.

68 conjugacy classes of subgroups.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#29509171	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₃₈₆₈	C₂	1	1	yes	maximal, characteristic, complemented
3	#29509160	C₂	1	2	yes	maximal, complemented
4	D₇₇₃₆	C₂	1	2	yes	maximal, complemented
5	M₁₆×C₉₆₇	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×D₉₆₇	—	2	1	no	—
7	Dic₁₉₃₄	C₂²	1	1	yes	characteristic, complemented
8	D₃₈₆₈	—	2	1	no	—
9	D₃₈₆₈	C₂²	1	2	yes	—
10	D₃₈₆₈	C₂²	1	1	yes	characteristic, complemented
11	C₂²⋊D₉₆₇	—	2	1	no	—
12	C₄×D₉₆₇	—	2	1	no	—
13	C₂×C₄×C₉₆₇	C₂²	1	1	yes	characteristic
14	C₈×C₉₆₇	C₂²	1	2	yes	complemented
15	C₂²×C₉₆₇	D₄	1	1	yes	characteristic
16	C₂×D₉₆₇	—	2	1	no	—
17	C₂×D₉₆₇	—	2	2	no	—
18	C₂×D₉₆₇	—	4	2	no	—
19	C₄×C₉₆₇	D₄	1	1	yes	characteristic
20	C₄×C₉₆₇	C₂³	1	1	yes	characteristic
21	Dic₉₆₇	—	2	1	no	—
22	C₂×C₉₆₇	—	2	1	no	—
23	C₂×C₉₆₇	C₂×D₄	1	1	yes	characteristic
24	D₉₆₇	—	4	1	no	—
25	D₉₆₇	—	4	2	no	—
26	C₉₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
27	AGL(1,ℤ/8)	—	967	1	no	maximal, Sylow
28	#41	—	967	1	no	—
29	C₂×D₄	—	967	1	no	—
30	SD₁₆	—	967	2	no	—
31	D₈	—	967	2	no	—
32	M₁₆	D₉₆₇	1	1	yes	characteristic, complemented
33	C₂³	—	1934	1	no	—
34	Q₈	—	967	1	no	—
35	D₄	—	1934	1	no	—
36	D₄	—	1934	1	no	—
37	D₄	—	967	1	no	—
38	D₄	—	967	2	no	—
39	C₂×C₄	—	1934	1	no	—
40	C₂×C₄	C₂×D₉₆₇	1	1	yes	characteristic
41	C₈	C₂×D₉₆₇	1	2	yes	complemented
42	C₂²	—	3868	2	no	—
43	C₂²	—	1934	1	no	—
44	C₂²	—	1934	2	no	—
45	C₂²	D₃₈₆₈	1	1	yes	characteristic
46	C₄	—	1934	1	no	—
47	C₄	D₃₈₆₈	1	1	yes	characteristic
48	C₄	C₂²×D₉₆₇	1	1	yes	characteristic
49	C₂	—	2	1	no	—
50	C₂	—	3868	2	no	—
51	C₂	—	3868	1	no	—
52	C₂	C₂×D₃₈₆₈	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₃₈₆₈
commutator, cosocle	C₄×C₉₆₇	C₂³
Frattini	C₄	C₂²×D₉₆₇
Fitting	M₁₆×C₉₆₇	C₂
socle	C₂×C₉₆₇	C₂×D₄
hypercenter	M₁₆	D₉₆₇
hypocenter	C₉₆₇	AGL(1,ℤ/8)
LCS	G ▷ C₄×C₉₆₇ ▷ C₂×C₉₆₇ ▷ C₉₆₇
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ M₁₆

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. #29509171	C₂	semidirect
2. C₂×D₃₈₆₈	C₂	semidirect
3. #29509160	C₂	semidirect
4. D₇₇₃₆	C₂	semidirect
5. M₁₆×C₉₆₇	C₂	semidirect
7. Dic₁₉₃₄	C₂²	semidirect
10. D₃₈₆₈	C₂²	semidirect
14. C₈×C₉₆₇	C₂²	semidirect
26. C₉₆₇	AGL(1,ℤ/8)	semidirect
32. M₁₆	D₉₆₇	semidirect
41. C₈	C₂×D₉₆₇	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
#29509171	2
C₂×D₃₈₆₈	2
#29509160	2
D₇₇₃₆	2
M₁₆×C₉₆₇	2
AGL(1,ℤ/8)	967